In modern applications, such as Electronic Voting, e-Health, e-Cash, there is a need that the validity of a signature should be verified by only one responsible person. This is opposite to the traditional digital signature scheme where anybody can verify a signature. There have been several solutions for this problem, the first one is we combine a signature scheme with an encryption scheme; the second one is to use the group signature; and the last one is to use the strong designated verifier signature scheme with the undeniable property. In this paper, we extend the traditional digital signature scheme to propose a new solution for the aforementioned problem. Our extension is in the sense that only a designated verifier (responsible person) can verify a signer’s signature, and if necessary (in case the signer refuses to admit his/her signature) the designated verifier without revealing his/her secret key is able to prove to anybody that the signer has actually generated the signature. The comparison between our proposed solution and the three existing solutions shows that our proposed solution is the best one in terms of both security and efficiency.